Leptonic and semileptonic charm decays at BESIII

The BESIII collaboration has achieved important measurements in charmed purely leptonic and semi-leptonic decays using data samples collected at center-of-mass energies of 3.773 GeV, 4.128-4.226 GeV, and 4.237-4.669 GeV. This proceeding presents recent BESIII results on charmed purely leptonic and semileptonic decays, including measurements of branching fractions, the Cabibbo-Kobayashi-Maskawa matrix elements $|V_{cs}|$ and $|V_{cd}|$, decay constants and form factors, as well as a test of the Lepton flavor universality.